In one of my experiments I got that whenever I have a significant granger causality, I have a high correlation. I was wondering if this is true in general. In particular, what confuses me is that when there is a perfect correlation between two sequences, the granger causality will be zero. In particular, the correlation between a sequence and itself is 1, while the granger causality is zero.
I would like to understand the expected relationship between the granger causality and correlation. does the first "influence" the second? Is it true that in general high causality implies high correlation but low causality doesn't have any indication about the correlation?